(a) Illustrate the sets U, A, B and C in a Venn diagram, marking all the elements in the appropriate places. (Note: if any region in your diagram does not contain any elements, re-draw the set loops to correct this.)

(b) Using your Venn diagram, list the elements in each of the following sets:

A ∩ B, A ∪ C, A′, B′, B ∩ A′, B ∩ C′, A – B, A Δ B

(c) Complete the statement using a single symbol: C - B = ... .

2

True or false?

(a) | ø | = 1

(b) | { x, x } | = 2

(c) | U ∩ ø | = 0

3

What can you say about two sets P and Q if:

(a) P ∩ Q′ = ø

(b) P ∪ Q = P?

Question 4

4

Make six copies of the Venn diagram shown alongside, and then shade the areas represented by:

(a) A ′ ∪ B

(b) A ∩ B ′

(c) (A ∩ B) ′

(d) A ′ ∪ B ′

(e) (A ∪ B) ′

(f) A ′ ∩ B ′

5

Identify the sets represented by each of the shaded areas below, using the set notation symbols ∩, ∪ and ′ only:

(a)

(b)

(c)

(d)

6

(a) One of the shaded regions in question 5 represents the set A – B. Identify which one it is, and hence write a definition of A – B using only symbols from the list ∩, ∪ and ′.

(b) Again using one of your answers to question 5, write a definition of A Δ B using only symbols from the list ∩, ∪ and ′. (There are two possibilities here – see if you can find them both!)